Given a dataset $X$ with $n=20$ observations, where $\sum_{i=1}^{20} x_i = 100$ and $\sum_{i=1}^{20} x_i^2 = 800$. If we define a transformed variable $Y = 2X - 5$, what are the mean $\bar{y}$ and variance $s_y^2$ of the new dataset?